Quasi-long-ranged order in two-dimensional active liquid crystals

Abstract

Quasi-long-ranged order is the hallmark of two-dimensional liquid crystals. At equilibrium, this property implies that the correlation function of the local orientational order parameter decays with distance as a power law: i.e., ∼|r|-ηp, with ηp a temperature-dependent exponent. While in general nonuniversal, ηp=1/4 universally at the Berezinskii-Kosterlitz-Thouless transition, where orientational order is lost because of the unbinding of disclinations. Here, we demonstrate that, in active liquid crystals, the notion of quasi-long-ranged order fundamentally differs from its equilibrium counterpart, and the exponent ηp is allowed to vary in the range 0<ηp≤2, with the upper bound corresponding to the isotropic phase. Our theoretical predictions are supported by a survey of a variety of experimental realizations of two-dimensional active liquid crystals.